Trigonometric Identity Subtraction

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I can't do problems such as $ \displaystyle \csc \theta - \sin \theta = \frac{\cos^2 \theta}{\sin \theta}$

Because I simply do not know how to deal with the 'subtraction' component involved. I don't even know how to subtract trigonometric fractions from each other. Can someone help here with respect to the question?

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2 Answers

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Hint: Finding a common denominator goes something like this: $\frac{1}{b} - a = \frac{1}{b} - \frac{ab}{b} = \frac{1-ab}{b}$ and $\csc{\theta} = \frac{1}{\sin{\theta}}$

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$\csc\theta - \sin\theta$

$=\frac{1}{\sin\theta} - \sin\theta$

$=\frac{1}{\sin \theta} - \frac{\sin^2 \theta}{\sin\theta}$

$=\frac{1-\sin^2 \theta}{\sin\theta}$

$=\frac{\cos^2 \theta}{\sin\theta}$

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